Preheat oven to 350°F (180°C). Spray a 13x9-inch baking pan with cooking spray. Line pan with parchment paper, letting excess extend over sides of pan.

For brownie: In the top of a double boiler, combine chocolate chips and butter. Cook over simmering water, stirring occasionally, until melted and smooth. Remove from heat; let mixture cool slightly. Whisk in sugars until combined.

In a medium bowl, whisk together flour, cocoa, and salt.

Gradually add beaten eggs to chocolate mixture, whisking until combined. Whisk in vanilla. Fold in flour mixture just until combined.

For cheesecake: In the bowl of a stand mixer fitted with the paddle attachment, beat cream cheese at medium speed until smooth. Add granulated sugar and flour; beat until combined, stopping to scrape paddle and bottom and sides of bowl. With mixer on low speed, add eggs, one at a time, beating until combined after each addition. Beat in vanilla.

Spread two-thirds of brownie batter into prepared pan. Dollop cheesecake mixture onto batter in pan, and gently spread smooth with an offset spatula. Dollop remaining brownie batter onto cheesecake mixture. Using a wooden pick, swirl together batter and cheesecake.

Bake until edges are set and an instant-read thermometer inserted in center registers 175°F (79°C) to 180°F (82°C), 50 to 55 minutes, covering with foil after 20 minutes of baking. Let cool completely in pan on a wire rack.

Using excess parchment as handles, remove from pan, and cut into bars. Store in an airtight container for up to 3 days.